26 ms·

Do wide and deep networks learn the same things?

107 points by MindGods 5y ago

sova 5y ago
At first I thought this had something to do with the classic "breadth vs. depth" notion on learning stuff -- if you're preparing for the MCAT it is better to have breadth that covers all the topics than depth in one or two particulars for the exam, but this is actually just about the dimensions of the neural network used to create representations. Naturally, one would expect a "sweet spot" or series of "sweet spots." From the paper at https://arxiv.org/pdf/2010.15327.pdf https://arxiv.org/pdf/2010.15327.pdf > As the model gets wider or deeper, we seethe emergence of a distinctive block structure— a considerable range of hidden layers that have very high representation similarity (seen as a yellow square on the heatmap). This block structure mostly appears in the later layers (the last two stages) of the network. I wonder if we could do similar analysis on the human brain and find "high representational similarity" for people who do the same task over and over again, such as play chess. Also, I don't really know what sort of data they are analyzing or looking at with these NN, maybe someone with better scansion can let me know?
- andersource 5y ago
  Haven't read thoroughly but it seems they are investigating ResNet models [0] trained for image classification. > We apply CKA to a family of ResNets of varying depths and widths, trained on common benchmark datasets (CIFAR-10, CIFAR-100 and ImageNet) [0] https://arxiv.org/abs/1512.03385 https://arxiv.org/abs/1512.03385
- verdverm 5y ago
  iirc, the human neocortex is only 6 layers deep with some interesting vertical connection structures, perhaps similar to skip connections in NN. It would be interesting to see where the deep vs wide analysis ends up when many problem types are used. Can a single network be trained on multiple problems at once and perform well on all?
  - ubercore 5y ago
    That sounds fascinating. When talking about something as complex and interconnected as a human neocortex, what does "only 6 layers deep" mean?
    - mattkrause 5y ago
      If you look at a slice of cortex under the microscope, there appear to be six physical layers (like a cake), owing to the different types, numbers, and arrangement of neurons in each. Canonically, the cortex is built out of columns, each of which repeat the same motif. Within a cortical column, signals enter a cortical region through layer IV, 'ascend' to other cortical areas via Layers II and III, and project elsewhere in the brain via Layer V/VI. Layer I mostly contains passing fibers going elsewhere. There are also "horizontal" or lateral connections between and within columns. This is sort of an abstraction though. It's often hard to clearly delineate the boundary between Layer II and III. Layer IV of primary visual cortex has many small sublayers (4C alpha), but it's very very small in others.
  - Buttons840 5y ago
    I'm not sure what skip connections are, but I think I have a good guess as to what they are. I've wanted to try a neural network where the output of every layer goes into every subsequent layer. Each layer would thus provide a different perspective to subsequent layers. Anyone know if this has been tried?
    - verdverm 5y ago
      Have a look at AlphaStar, it's a pretty interesting network of networks that has some skip functionality. The DeepMind lecture series on YouTube is pretty great. You'd likely overdue it with skips everywhere, too many connections to learn and backprop on that learning would likely be difficult
    - nomad225 5y ago
      Densely Connected Convolutional Networks (https://arxiv.org/abs/1608.06993 https://arxiv.org/abs/1608.06993) use the idea you're talking about quite effectively.
rajansaini 5y ago
Those are very interesting empirical results. This lecture explains the deeper vs shallow tradeoff theoretically: https://www.youtube.com/watch?v=qpuLxXrHQB4 https://www.youtube.com/watch?v=qpuLxXrHQB4. He's an amazing lecturer; wish I didn't need subtitles! (If you're too lazy to watch, it turns out that there exist functions that a shallow network can never approximate)
godelski 5y ago
For more context to people, we have the universal approximation theorem for neural nets that basically says if a network is wide enough it can approximate anything (with at least 2 layers). So a lot of stuff was really wide. Then VGG[0] came out and showed that deep networks were very effective (along with other papers, things happen in unison. Leibniz and Newton). Then you get ResNets[1] with skip connections and move forward to today. Today we've started looking more at what networks are doing and where their biases lie. This is because we're running into some roadblocks with CNNs vs Transformers. They have different inductive biases. Vision transformers still aren't defeating CNNs, but they are close and it is clear they learn different things. So we're seeing more papers doing these types of analyses. ML will likely never be fully interpretable, but we're getting better at understanding. This is good because a lot of times picking your model and network architecture is more art than science (especially when choosing hyper parameters). [0] https://arxiv.org/abs/1409.1556 https://arxiv.org/abs/1409.1556 [1] https://arxiv.org/abs/1512.03385 https://arxiv.org/abs/1512.03385
- joe_the_user 5y ago
  Deep networks have also been shown to be universal, just FYI,
  - godelski 5y ago
    Oh yes, sorry if it gets interpreted otherwise. It is too late to edit for that clarity but thanks for the note.
- dimatura 5y ago
  I would say AlexNet [1], rather than VGG, was the landmark paper that got the computer vision community to pay attention to deep learning, specifically by winning the 2012 imagenet competition by a large margin. Not that there weren't successes before (specifically, deep nets had also been getting traction in speech processing), and of course deep learning itself is much older than alexnet. But I think most people, specially in vision, would say the 2012 imagenet competition was the watershed moment for DL. By current standards it's not very deep, but at the time it was definitely "deeper"than the popular models at the time (which were mostly not neural networks). VGG is also super influential of course -- it reinforced the trend towards ever deeper networks, which ResNet also took to another level. [1] https://papers.nips.cc/paper/4824-imagenet-classification-with-deep-convolutional-neural-networks.pdf https://papers.nips.cc/paper/4824-imagenet-classification-wi...
joe_the_user 5y ago
So, it seems like the "blocks" they're talking about are basically redundancies, duplicated logic. It makes sense to me that since they provide the same functionality, how or how these duplicates exist doesn't matter. But I'm an amateur

107 points by MindGods 5y ago

sova 5y ago

At first I thought this had something to do with the classic "breadth vs. depth" notion on learning stuff -- if you're preparing for the MCAT it is better to have breadth that covers all the topics than depth in one or two particulars for the exam, but this is actually just about the dimensions of the neural network used to create representations. Naturally, one would expect a "sweet spot" or series of "sweet spots." From the paper at https://arxiv.org/pdf/2010.15327.pdf https://arxiv.org/pdf/2010.15327.pdf > As the model gets wider or deeper, we seethe emergence of a distinctive block structure— a considerable range of hidden layers that have very high representation similarity (seen as a yellow square on the heatmap). This block structure mostly appears in the later layers (the last two stages) of the network. I wonder if we could do similar analysis on the human brain and find "high representational similarity" for people who do the same task over and over again, such as play chess. Also, I don't really know what sort of data they are analyzing or looking at with these NN, maybe someone with better scansion can let me know?

andersource 5y ago
Haven't read thoroughly but it seems they are investigating ResNet models [0] trained for image classification. > We apply CKA to a family of ResNets of varying depths and widths, trained on common benchmark datasets (CIFAR-10, CIFAR-100 and ImageNet) [0] https://arxiv.org/abs/1512.03385 https://arxiv.org/abs/1512.03385
verdverm 5y ago
iirc, the human neocortex is only 6 layers deep with some interesting vertical connection structures, perhaps similar to skip connections in NN. It would be interesting to see where the deep vs wide analysis ends up when many problem types are used. Can a single network be trained on multiple problems at once and perform well on all?
- ubercore 5y ago
  That sounds fascinating. When talking about something as complex and interconnected as a human neocortex, what does "only 6 layers deep" mean?
  - mattkrause 5y ago
    If you look at a slice of cortex under the microscope, there appear to be six physical layers (like a cake), owing to the different types, numbers, and arrangement of neurons in each. Canonically, the cortex is built out of columns, each of which repeat the same motif. Within a cortical column, signals enter a cortical region through layer IV, 'ascend' to other cortical areas via Layers II and III, and project elsewhere in the brain via Layer V/VI. Layer I mostly contains passing fibers going elsewhere. There are also "horizontal" or lateral connections between and within columns. This is sort of an abstraction though. It's often hard to clearly delineate the boundary between Layer II and III. Layer IV of primary visual cortex has many small sublayers (4C alpha), but it's very very small in others.
- Buttons840 5y ago
  I'm not sure what skip connections are, but I think I have a good guess as to what they are. I've wanted to try a neural network where the output of every layer goes into every subsequent layer. Each layer would thus provide a different perspective to subsequent layers. Anyone know if this has been tried?
  - verdverm 5y ago
    Have a look at AlphaStar, it's a pretty interesting network of networks that has some skip functionality. The DeepMind lecture series on YouTube is pretty great. You'd likely overdue it with skips everywhere, too many connections to learn and backprop on that learning would likely be difficult
  - nomad225 5y ago
    Densely Connected Convolutional Networks (https://arxiv.org/abs/1608.06993 https://arxiv.org/abs/1608.06993) use the idea you're talking about quite effectively.

rajansaini 5y ago

Those are very interesting empirical results. This lecture explains the deeper vs shallow tradeoff theoretically: https://www.youtube.com/watch?v=qpuLxXrHQB4 https://www.youtube.com/watch?v=qpuLxXrHQB4. He's an amazing lecturer; wish I didn't need subtitles! (If you're too lazy to watch, it turns out that there exist functions that a shallow network can never approximate)

godelski 5y ago

For more context to people, we have the universal approximation theorem for neural nets that basically says if a network is wide enough it can approximate anything (with at least 2 layers). So a lot of stuff was really wide. Then VGG[0] came out and showed that deep networks were very effective (along with other papers, things happen in unison. Leibniz and Newton). Then you get ResNets[1] with skip connections and move forward to today. Today we've started looking more at what networks are doing and where their biases lie. This is because we're running into some roadblocks with CNNs vs Transformers. They have different inductive biases. Vision transformers still aren't defeating CNNs, but they are close and it is clear they learn different things. So we're seeing more papers doing these types of analyses. ML will likely never be fully interpretable, but we're getting better at understanding. This is good because a lot of times picking your model and network architecture is more art than science (especially when choosing hyper parameters). [0] https://arxiv.org/abs/1409.1556 https://arxiv.org/abs/1409.1556 [1] https://arxiv.org/abs/1512.03385 https://arxiv.org/abs/1512.03385

joe_the_user 5y ago
Deep networks have also been shown to be universal, just FYI,
- godelski 5y ago
  Oh yes, sorry if it gets interpreted otherwise. It is too late to edit for that clarity but thanks for the note.
dimatura 5y ago
I would say AlexNet [1], rather than VGG, was the landmark paper that got the computer vision community to pay attention to deep learning, specifically by winning the 2012 imagenet competition by a large margin. Not that there weren't successes before (specifically, deep nets had also been getting traction in speech processing), and of course deep learning itself is much older than alexnet. But I think most people, specially in vision, would say the 2012 imagenet competition was the watershed moment for DL. By current standards it's not very deep, but at the time it was definitely "deeper"than the popular models at the time (which were mostly not neural networks). VGG is also super influential of course -- it reinforced the trend towards ever deeper networks, which ResNet also took to another level. [1] https://papers.nips.cc/paper/4824-imagenet-classification-with-deep-convolutional-neural-networks.pdf https://papers.nips.cc/paper/4824-imagenet-classification-wi...

joe_the_user 5y ago

So, it seems like the "blocks" they're talking about are basically redundancies, duplicated logic. It makes sense to me that since they provide the same functionality, how or how these duplicates exist doesn't matter. But I'm an amateur